Method and apparatus for analyzing semiconductors

ABSTRACT

A semiconductor wafer is analyzed by applying successive values of reverse-bias voltage V to a diode region to form successive depletion layers of different depth X. Current of frequency f1 is applied to the diode and detected to determine X. Voltage at frequency f2, which is lower than f1, is applied to the diode such as to produce a modulation Delta E2 of the electric field in the depletion layer and a modulation Delta X2 of the depletion layer depth. The voltage input at frequency f2 is controlled to maintain either Delta E2 or Delta X2 constant with changes of X, and the modulation of the f1 voltage at frequency f2 is measured to determine one of these semiconductor parameters at different values of X. In this manner, a profile of semiconductor carrier density N, or its reciprocal 1/N, can be determined. An improved method of determining X is also disclosed.

ilited States Eatet [1 1 Miller [54] METHOD AND APPARATUS FOR ANALYZING SEMTCONDUCTORS Inventor: Gabriel Lorimer Miller, Westfield,

[73] Assignee: Bell Telephone Laboratories, Incorporated, Murray Hill, Berkeley Heights, NJ.

Filed: May 28, 1971 Appl. No.: 147,846

U.S. Cl ..324/l58 D, 324/158 T Int, Cl. ..G0lr 31/26 Field of Search ..324/l58 D, 158 T,

[56] References Cited UNITED STATES PATENTS 9/1971 Copeland ..324/l58 D 6/1960 Rutz ..29/574 6/1970 Copeland ..324/l58 R OTHER PUBLICATIONS IEEE Trans. on

VOLTAG E SQUARE WAVE Primary ExaminerRudolph V. Rolinec Assistant Examiner-Ernest F. Karlsen AttorneyR. J. Guenther and Arthur J. Torsiglieri 57 ABSTRACT A semiconductor wafer is analyzed by applying successive values of reverse-bias voltage V to a diode region to form successive depletion layers of different depth X. Current of frequency f is applied to the diode and detected to determine X. Voltage at frequency f which is lower than f is applied to the diode such as to produce a modulation AE- of the electric field in the depletion layer and a modulation AX of the depletion layer depth. The voltage input at frequency f is controlled to maintain either AE or AX constant with changes of X, and the modulation of the f voltage at frequency f is measured to determine one of these semiconductor parameters at different values of X. In this manner, a profile of semiconductor carrier density N, or its reciprocal l/N, can be determined. An improved method of determining X is also disclosed.

14 Claims, 8 Drawing Figures |9 OF AMPLITUDE Avg I 25 V PROPORTIONAL TO x CHOPPER {2 g r tswficm SOURCE ADDER 2| f PHASE 20 f SOURCE DETECTOR 28 (CONSTANT B g vg gf CURRENT) LOW PASS 29 vmvz 23 .FILTER DETECTOR 14 |3 fi VOLTAGE Low PASS PROPORTIONAL VOLTAGE PROPORTIONAL FILTER '/N TO DEPLETION LAYER THICKNESS x I I2 I l f DISTANCE PATENTED MAY 1 I973 SHEET 3 OF 4 VOLTAG FIG 4 BIAS 55 VOLTAGE ROPgguo 5| DETECTOR REFERENCE '4 4s 50 SOURCE M 49 "*i 1 PHA E LOW DT c g PASS -'-COMPARATOR T -2 47 FILTER A 7 5 VARIABLE /46 2 ATTENUATOR 45 fi SOURCE/ (CONSTANT PH VOLTAGE) SHI BIAS FIG. 5 OLTAGE 5| i R RENCE I); 49 5O 5 RCE I I Low G k 2% s -C0MPARATOR ER F T 47 52 CHOPPER 57 LTA OR AL TO x 0 R E C PHASE vo SHIFTER PATENTED 1 I975 SHEET UF 4 METHOD AND AIPARATUS FOR ANALYZING SEMICONDUCTORS BACKGROUND OF THE INVENTION This invention relates to methods and apparatus for analyzing semiconductor wafers, and more particularly, to apparatus for determining a profile of the variation of carrier density with distance in a semiconductor wafer.

An important step in the fabrication of semiconductor devices and integrated circuits is a determination of the majority carrier distribution, also known as the doping density profile, in a semiconductor wafer. A small metal contact is typically bonded to a top surface of the wafer to form a Schottky barrier diode. A varying reverse-bias voltage is applied across the diode and the capacitance of the diode is measured as a function of bias voltage. The carrier density profile is related by a known expression to the capacitance and to the rate of change of capacitance with bias voltage, and is therefore determinable. However, the technique requires computation, either manually or by a computer, and is limited in resolution and numerical accuracy by the necessity to interpolate between two points to find the rate of change of capacitance.

A different approach is described in the US. Pat. of Copeland No. 3,518,545 issued June 30, 1970, and assigned to Bell Telephone Laboratories, Incorporated. The diode is reverse-biased, a constant A.C. current is directed through the diode, and first and second harmonic voltages across the diode are measured. It can be shown that the first harmonic voltage is proportional to the thickness of the diode depletion layer while the second harmonic voltage is proportional to the reciprocal of carrier density at the outer boundary of the depletion layer. By changing the reverse-bias voltage, the outer boundary of the depletion layer can be made to scan through the wafer thickness, and the reciprocal of carrier density can be determined at successive depth in the wafer. While the Copeland technique is clearly superior in most respects to conventional methods, I have devised a different alternative approach that offers several additional advantages.

SUMMARY OF THE INVENTION In accordance with the present invention, a semiconductor wafer is analyzed by applying successive values of reverse-bias voltage V to a diode region, as in previous techniques, to form successive depletion layers of different depth X. Frequency f current of constant magnitude is applied to the diode and the resulting diode voltage may be detected to determine depth X as in the Copeland technique. Voltage at a frequency f which is lower than f is applied to the diode such as to produce a modulation AE of the electric field in the depletion layer, and a modulation AX of the depletion layer depth. A major feature of the invention is predicated on the observation that, under these conditions, the carrier density N is a function of both AX and A5,. Thus, carrier density N may theoretically be determined by maintaining AX constant and measuring (IE or conversely, maintaining AE, constant and measuring AX In practice, one of the two modulation parameters can conveniently be maintained constant with changes of depletion layer depth X by properly feeding back a portion of the energy directed through the diode region. In one embodiment, the low frequency f voltage is controlled by the detected output at frequency f so as to be proportional to the depletion layer depth X. It can be shown that, when the voltage at f is proportional to X, the electric field modulation AE is constant with changes of X, and the reciprocal of the doping density is proportional to AX In turn, AX is a function of diode reactance, and its value can be determined by measuring the modulation of the f signal across the diode at frequency f More specifically, the magnitude of the modulation of the f voltage at frequency f; is a measure of the reciprocal of the carri- 5 er density l/N at the edge of the depletion layer.

In an alternative embodiment, the magnitude of the f voltage is adjusted by a feedback loop in such a way as to keep AX constant. With AX constant, the magnitude of the electric field variation at frequency f is proportional to N, the carrier density at the edge of the depletion layer.

In accordance with another feature of the invention, the capacitive component of the current through the diode is maintained at a constant value by phase detection, comparison of the resulting DC. with a reference, and thereby generating a control signal to adjust the amplitude of the f drive. This feedback technique yields a more dependable and accurate value of X because it does not require the approximation of a constant current source as a circuit element and, in addition, it is substantially independent of shunt resistive components of the diode impedance.

In another embodiment, the f source operates a chopper which passes control signal current to the diode. With this arrangement, the control signal voltage itself may be taken as the voltage proportional to X, thereby avoiding the need for an accurate f detector.

It will be seen that my method and apparatus offer the same advantages as the Copeland technique; that is, it is simple, accurate and permits a continuous or realtime indication of carrier density with respect to distance. In addition, it offers certain other advantages. For example, since it admits of phase locked detectors, the effects of possible drifts in oscillator frequencies are minimized. The spurious effects of leakage currents and stray reactances'can be substantially reduced (allowing the device under test to be mounted at the end of long coaxial cables), and the system noise bandwidth can be most easily controlled.

These and other objects, features, and advantages of the invention will be better understood from a consideration of the following detailed description taken in conjunction with the accompanying drawing.

DRAWING DESCRIPTION FIG. 1 is a schematic diagram of a diode region of part of a wafer that is being evaluated in accordance with an illustrative embodiment of the invention;

FIG. 2 is a functional block diagram of apparatus for evaluating a diode region of a semiconductor wafer in accordance with one embodiment of the invention;

FIG. 3 is a functional block diagram of apparatus for analyzing a semiconductor wafer in accordance-with another embodiment of the invention;

FIG. 4, 5, and 6 are block diagrams illustrating different methods for determining depletion layer depth by directing a constant A.C. current through a diode region; and

FIG. 7 is a schematic diagram of a presently preferred embodiment of the invention.

DETAILED DESCRIPTION Referring now to FIG. 1 there is shown in section a portion of a semiconductor wafer 11 having a certain carrier density N that varies as a function of distance X, as typically shown by curve 12. As a first step in determining curve 12, a Schottky barrier contact 13 is formed on one surface of the wafer to form a diode region 14. The diode region is reverse-biased to form a depletion layer having a thickness X. As with most such techniques, the present invention is a process for determining the carrier density at the boundary 15 of the depletion layer. By changing the reverse-bias voltage, the depletion layer thickness X changes, causing boundary 15 to scan through the wafer to permit successive points on curve 12 to be determined.

In accordance with the invention, a low frequency voltage of frequency f is applied to the diode region to cause an oscillation of the depletion layer boundary between locations 15 and 15'. During each cycle, thef bias voltage of amplitude AV increases the electric field in the depletion layer by an amount AE given by the equation AE =AV /X. (l) The resulting increase in depletion layer thickness to X AX must uncover an additional quantity of charge qN AX satisfying the relation 1 A WAE It is apparent from relationship (3) that, if AX were kept constant, AE would be proportional to N, whereas if AE were kept constant, AX would be proportional to UN.

Referring now to FIG. 2, there is shown a functional block diagram of apparatus for maintaining LtE constant so that AX is directly proportional to 1/N. As will be seen later, with AE constant, UN is determined by measuring the magnitude of the modulation of the f, signal at frequency f A diode portion 14 of a semiconductor wafer 11 is analyzed by driving an XY plotter 18 to generate a curve 12 of the reciprocal of carrier density variation with distance. A reverse-bias voltage V is applied to the diode 14 by a source 19 viaan adder 20. Also applied to the diode is constant-current A.C.energy of a high tion layer thickness. A detector 23 converts thef voltage to a DC. voltage proportional to the distance X as shown in the drawing. As will be explained later, this is not the preferred method of generating the DC. voltage proportional to X, but merely serves as an illustration.

In accordance with the invention, the voltage proportional to X is used to control the amplitude of a low frequency f from a source 25 that is directed to the diode 14. A convenient method for obtaining an amplitude proportional to X at frequency f is to use the f source 25 to operate a switch or chopper 26. Chopper 26 then periodically passes D.C. voltage from detector 23 to generate a square wave of frequency f and an amplitude AV proportional to the depletion layer thickness X. This voltage is combined by adder 20 with the bias voltage V to give a combined bias voltage V AV The incremental voltage AV of course results in the incremental depletion layer thickness AX and incremental electric field AE referred to before. It is important that the frequency f be small compared to f for example, f may be cps with an f frequency of I megahertz.

During the analysis of the wafer 11, the variable bias source 19 is operated to give successively larger D.C. reverse-bias voltages V, with successively thicker depletion layers. As the depletion layer thickness X increases, AV increases proportionately. Thus, by equation (1), the modulation parameter AE is maintained constant. Then, by equation (3), the incremental distance AX depicted in FIG. 1 is proportional to UN. Since the incremental distance AX modulates the diode impedance, its value can be determined by measuring the magnitude of the modulation of the f voltage across the diode at frequency f The magnitude of the modulation of the f signal is detected by the combination of phase detector 28 and low pass filter 29 which together generate a DC. voltage proportional to the magnitude of the voltage at frequencyf The output voltage of filter 29 is then proportional to the parameter UN and constitutes the Y input to the XY plotter 18.

It should be noted that using phase detector 28 to detect the magnitude of the frequency f voltage offers substantial advantages over other detection methods because it is insensitive to signals at frequencies other than f and, in addition, the post-detection filter 29 defines the system bandwidth in a very convenient way. Further, phase detection reduces the sensitivity of the apparatus to oscillator frequency variations; i.e., both inputs to phase detector 28 track any frequency deviation of source 25 to give an accurate output to the plotter 18.

FIG. 3 shows an alternative method ofgenerating a carrier density profile in which the modulation parameter AX is maintained constant with changes of depletion layer thickness X. As before, the DC. bias from a source 31 is varied to give a changing depletion layer thickness X which is determined by detecting the voltage across the diode region at frequency f A low frequency component is added to the diode bias from a source 35 via a variable attenuator 36 and an adder 37. The f, modulation again produces the modulation AX, of the depletion layer thickness in the diode, and the resulting modulation of the f voltage across the diode at frequency f, is indicative of AX The low frequency f signal is detected by a phase detector 39 which generates an output proportional to AX The output of detector 39 is directed to a comparator 40 which compares it with a reference voltage from a source 41. The output of the comparator 40 drives the variable attenuator 36 which controls the magnitude of f current directed through the diode. The comparator 40 is essentially a subtracting device, its output being proportional to the difference between the reference voltage and the voltage proportional to AX Hence, since the reference voltage is constant, its effect is to control the output AV of variable attenuator 36 such as to maintain a constant modulation AX with changes in the depletion layer thickness X.

With AX constant, AE is directly proportional to the carrier density N, by equation (3). AV is in turn indicative of AE by equation (1), and so AV may be divided by X, using an analog divider 63, to provide a voltage proportional to N for display by the XY plotter, as shown in the drawing.

Feedback can similarly be used to maintain the constant f current required for dependably developing a voltage proportional to X. As is pointed out in the Copeland patent, a constant current source can only be approximated; and therefore the sources 21 and 32 of FIG. 2 and 3 are inherently subject to error. FIG. 4 and 5 are circuits for providing a constant f current through the diode region by controlling the magnitude of f voltage across the diode.

In FIG. 4, f current from a constant voltage source 45 is directed to the diode of region 14 via a variable attenuator 46. A high gain amplifier 47 causes virtually all of the diode current to flow through a resistor 48. The f current through the diode is detected by a phase detector 49 and a smoothing filter 50, and compared to a reference voltage from a source 51 in a comparator 52. If the f current deviates from the reference value, an error signal is fed back to the variable attenuator 46 to control the voltage delivered from source 45. In this way, the capacitive component of the current through the diode 14 is maintained at a constant value.

By principles known in the art, the input to high gain amplifier 47 is at a virtual ground potential. As a result, the entire f voltage across the diode region appears at the input to the diode region; thus, f voltage detected by a detector 55 is indicative of depletion layer thickness X as shown.

It would-additionally be desirable to eliminate the f of the comparator output but converted to frequencyf by chopper 57. The current through the diode at frequencyf is constant, as before. The voltage at the output of the comparator required to keep the f diode current constant depends on the diode depletion layer width, and can therefore be taken as being proportional to X as shown.

The elimination off detector 55 of FIG. 4 from the circuit of FIG. 5 is of significant importance because it circumvents the problem of detector linearity in providing the X signal. Detection in the circuit of FIG. 5 is by phase detector 49, and consequently if the frequency of f should vary detector 49 tracks such variations. In addition, the system is only sensitive to the capacitive part of the current flowing through device 14. Because of these advantages, the circuit of FIG. 5 is presently the preferred method of generating the voltage proportional to X required by the inventron.

FIG. 6 shows still another alternative method of generating an output voltage proportional to X. With the diode 14 connected in parallel with the high gain amplifier 61, as shown, the output voltage V can be shown to be given by:

0 1) 1 (4) where Z is the impedance of diode 14, Z is the impedance of capacitor 60, and V is the constant voltage output of the f source. With Z and V, being constant the output voltage V is directly proportional to the diode impedance Z which, in turn, is proportional to depletion layer thickness X. Thus, the output voltage V can be calibrated in terms of X. This embodiment is not preferred, however, because spurious diode shunt resistances can have the effect of reducing the magnitude of bias changes AV seen by the diode, which leads to difficulties in interpretation of the profile data.

FIG. 7 is a circuit diagram of a wafer analyzing circuit that has been built incorporating the circuit of FIG. 5 (for generating the X output) with the circuit of FIG. 2 (for generating the Y output). Reference numerals from FIGS. 5 and 2 are included in FIG. 7 for assistance in tracing the circuit functions. The circuit incorporates numerous design features which, for the sake of brevity, will not be described or explained. The values of the various circuit elements are designated by the accepted notations: pf picofarads, pf microfarads, K kilohms. The frequency f was 0.7 megahertz, andf was I50 hertz. Noteworthy features of the FIG. 11 circuit are as follows:

1. Since phase detection is employed, the system is substantially independent of shunt resistive components of the diode current.

2. No complex analog operations are involved; only linear amplifiers and switches are employed in deriving both X and l/N.

3. Since the system is phase locked, it is substantially independent of drifts of the oscillator frequencies.

4. Capacitances at the input of amplifier 47, or at the output of the low impedance adder 20, are of little consequence, and so the diode can be mounted at the end of long coaxial cables if desired.

5. The effect of stray shunt capacitance across the diode under test can be removed by adjusting capacitor C, following the inverting amplifier A4;

6. The electronics are relatively simple, requiring the use of only medium speed operational amplifiers, together with field effect transistor switches for the choppers and phase detectors.

Many tests have been made using the circuit of FIG. 7 on devices having known doping profiles. Accuracy and long term stability have been shown to be excellent. A number of different experiments have been carried out, such as on-line monitoring of radiation damage during accelerator implantations. Such experiments have been much more difficult or impossible using other doping profiling techniques.

The various embodiments and procedures described are considered to be merely illustrative of the inventive concepts involved. Numerous other embodiments and modifications may be made by those skilled in the art without departing from the spirit and scope of the invention.

What is claimed is: l. A process for analyzing a semiconductor wafer comprising the steps of:

forming a diode region in the wafer; successively applying different values of reverse-bias voltage V to the diode region, thereby forming successive depletion layers of different depth X;

applying a constant A.C. current of frequency f to the diode region; detecting the voltage across the diode region at frequency f said voltage being indicative of the depletion layer depth X;

applying a voltage of frequency f to the diode region, said frequency f being small compared to f said voltage resulting in a modulation parameter AX equal to the variation in depletion layer depth, and a modulation parameter AE equal to the variation of electric field in the depletion layer;

maintaining one of the modulation parameters constant with changes of depletion layer depth X, and

detecting the modulation of the f signal at frequency f for different values of bias voltage V, thereby to evaluate the diode region at different depths.

2. The process of claim 1 wherein:

the step of maintaining a modulation parameter constant comprises the step of using said voltage at frequency f to control the voltage at frequency f;,. 3. The process of claim 2 wherein: the step of detecting frequency f voltage comprises the step of generating a'D.C. voltage proportional to the detected frequency f voltage; and

the step of controlling f voltage comprises the step of causing the DC voltage to be interrupted at frequency f whereby the applied diode region voltage V AV maintains a constant modulation parameter AE with changes of X, and-the detected f voltage is indicative of the reciprocal of carrier density 1/N at the edge of the depletion layer.

'4. The process of claim 3 wherein:

the fl, voltage across the diode is detected by phase detection.

5. The process of claim 2 wherein:

the step of detecting frequency f comprises the step of generating a D.C. voltage AV proportional to the detected f voltage; and

the step of modulating frequency f energy comprises the step of comparing AV with a reference voltage, generating a control signal proportional to the difference of the reference voltage and AV, and controlling the amplitude of frequency f with said control signal, whereby the parameter AX is maintained constant at changing values ofX and the detected f voltage is indicative of carrier density N at the edge of the depletion layer.

6. The process of claim 2 wherein:

in a semiconductor diode region comprising the steps of:

applying a bias voltage V to the diode, thereby establishing a depletion region in the diode of depth X generating a voltage AV proportional to X;

adding AV to V and applying to the diode a bias voltage V AV, thereby establishing a depletion region of depth X AX; and

measuring the parameters X and AX thereby to determine respectively the depletion region depth X and the reciprocal of free carrier density l/N at the edge of the depletion region.

8. The process of claim 7 wherein:

the step of measuring the distance X comprises the step of applying to the diode a constant A.C. current of frequency f and detecting the amplitude of the voltage across the diode region at frequency f,, said amplitude being indicative of the depletion region depth X,

9. The process of claim 8 wherein:

the step of measuring AX comprises the steps of adding voltage AV to bias voltage V intermittently at a frequency f and detecting the amplitude of the modulation of frequency f across the diode region at frequency f said amplitude being indicative of the parameter 1/N 10. The process of claim 8 further comprising the steps of:

applying progressively different bias voltages V to the diode region; and

repeating said steps after applying each different'bias voltage, thereby to determine the reciprocal of the free carrier density at a succession of different depletion layer depths and to determine a carrier density profile of the diode region.

1 1. The process of claim 10 wherein:

the frequencyf is much smaller thanf 12. The process of claim 10 wherein:

the step of applying to the diode region a constant A.C. current at frequency f comprises the steps of comparing f current through the diode with a reference current to generate a control signal, and controlling said f current with said control signal.

13. The process of claim 10 wherein:

the step of applying to the diode region A.C. current frequency f comprises the steps of comparing f current through the diode region with a reference current to generate a control current, causing said control current to be interrupted at frequency f and directing said interrupted control current through the diode region.

14. The process for determining a profile of the freecarrier density in a semiconductor diode region comprising the steps of:

successively applying different values of bias voltage of V to the diode region, thereby to form successive depletion layers of different depth X;

applying A.C. current of frequency f to the diode region detecting the f frequency voltage across the diode region;

measuring the f frequency voltage at different values of bias voltage V to determine corresponding values of depletion layer depth X:

applying AC. voltage of frequency f to the diode region, the f frequency being significantly smaller than f and resulting in a modulation AX of the depletion layer depth and in modulation AE of the electric field in the depletion layer;

maintaining the electric field modulation Al-T. sub- 

1. A process for analyzing a semiconductor wafer comprising the steps of: forming a diode region in the wafer; successively applying different values of reverse-bias voltage V to the diode region, thereby forming successive depletion layers of different depth X; applying a constant A.C. cuRrent of frequency f1 to the diode region; detecting the voltage across the diode region at frequency f1, said voltage being indicative of the depletion layer depth X; applying a voltage of frequency f2 to the diode region, said frequency f2 being small compared to f1, said voltage resulting in a modulation parameter Delta X equal to the variation in depletion layer depth, and a modulation parameter Delta E equal to the variation of electric field in the depletion layer; maintaining one of the modulation parameters constant with changes of depletion layer depth X, and detecting the modulation of the f1 signal at frequency f2 for different values of bias voltage V, thereby to evaluate the diode region at different depths.
 2. The process of claim 1 wherein: the step of maintaining a modulation parameter constant comprises the step of using said voltage at frequency f1 to control the voltage at frequency f2.
 3. The process of claim 2 wherein: the step of detecting frequency f1 voltage comprises the step of generating a D.C. voltage proportional to the detected frequency f1 voltage; and the step of controlling f2 voltage comprises the step of causing the D.C. voltage to be interrupted at frequency f2, whereby the applied diode region voltage V + Delta V2 maintains a constant modulation parameter Delta E with changes of X, and the detected f2 voltage is indicative of the reciprocal of carrier density 1/N at the edge of the depletion layer.
 4. The process of claim 3 wherein: the f2 voltage across the diode is detected by phase detection.
 5. The process of claim 2 wherein: the step of detecting frequency f1 comprises the step of generating a D.C. voltage Delta V proportional to the detected f1 voltage; and the step of modulating frequency f2 energy comprises the step of comparing Delta V with a reference voltage, generating a control signal proportional to the difference of the reference voltage and Delta V, and controlling the amplitude of frequency f2 with said control signal, whereby the parameter Delta X is maintained constant at changing values of X and the detected f2 voltage is indicative of carrier density N at the edge of the depletion layer.
 6. The process of claim 2 wherein: the step of applying to the diode region a constant A.C. current at frequency f1 comprises the steps of comparing f1 current through the diode with a reference current to generate a control signal, and controlling said f1 current with said control signal.
 7. The process for measuring the free carrier density in a semiconductor diode region comprising the steps of: applying a bias voltage V to the diode, thereby establishing a depletion region in the diode of depth X generating a voltage Delta V proportional to X; adding Delta V to V and applying to the diode a bias voltage V + Delta V, thereby establishing a depletion region of depth X + Delta X; and measuring the parameters X and Delta X thereby to determine respectively the depletion region depth X and the reciprocal of free carrier density 1/N at the edge of the depletion region.
 8. The process of claim 7 wherein: the step of measuring the distance X comprises the step of applying to the diode a constant A.C. current of frequency f1; and detecting the amplitude of the voltage across the diode region at frequency f1, said amplitude being indicative of the depletion region depth X.
 9. The process of claim 8 wherein: the step of measuring Delta X comprises the steps of adding voltage Delta V to bias voltage V intermittently at a frequency f2, and detecting the amplitude of the modulation of frequency f1 acRoss the diode region at frequency f2, said amplitude being indicative of the parameter 1/N
 10. The process of claim 8 further comprising the steps of: applying progressively different bias voltages V to the diode region; and repeating said steps after applying each different bias voltage, thereby to determine the reciprocal of the free carrier density at a succession of different depletion layer depths and to determine a carrier density profile of the diode region.
 11. The process of claim 10 wherein: the frequency f2 is much smaller than f1.
 12. The process of claim 10 wherein: the step of applying to the diode region a constant A.C. current at frequency f1 comprises the steps of comparing f1 current through the diode with a reference current to generate a control signal, and controlling said f1 current with said control signal.
 13. The process of claim 10 wherein: the step of applying to the diode region A.C. current frequency f1 comprises the steps of comparing f1 current through the diode region with a reference current to generate a control current, causing said control current to be interrupted at frequency f1, and directing said interrupted control current through the diode region.
 14. The process for determining a profile of the free-carrier density in a semiconductor diode region comprising the steps of: successively applying different values of bias voltage of V to the diode region, thereby to form successive depletion layers of different depth X; applying A.C. current of frequency f1 to the diode region detecting the f1 frequency voltage across the diode region; measuring the f1 frequency voltage at different values of bias voltage V to determine corresponding values of depletion layer depth X: applying A.C. voltage of frequency f2 to the diode region, the f2 frequency being significantly smaller than f1, and resulting in a modulation Delta X2 of the depletion layer depth and in modulation Delta E2 of the electric field in the depletion layer; maintaining the electric field modulation Delta E2 substantially constant, comprising the step of generating a voltage Delta V proportional to depletion layer depth X and using said voltage Delta V to control the magnitude of applied frequency f2 voltage; and measuring frequency f2 modulation of the f1 voltage across the diode region at different values of bias voltage V to determine the carrier density reciprocal 1/N at successive depths in the diode region. 